Q.66

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Found in: Page 834

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# Particle accelerators, such as the Large Hadron Collider, use magnetic fields to steer charged particles around a ring. Consider a proton ring with 36 identical bending magnets connected by straight segments. The protons move along a -m-long circular arc as they pass through each magnet. What magnetic field strength is needed in each magnet to steer protons around the ring with a speed of ? Assume that the field is uniform inside the magnet, zero outside.

The strength of magnetic field needed

See the step by step solution

## Step 1: Cyclotron motion

The particle accelerator motion is specified as a particles travelling in a uniform circular motion perpendicular to the magnetism at a constant speed. The radius of the circular motion induced by the magnetization is connected to the motion's radius.

## Step 2: Radius of motion

Where q is the particle's charged, v is the particle's speed, B is the magnetic field, and m is the particle's mass. Since a magnet has such a length of, the length of a circular pattern composed of 36 magnets will be, which matches the circumference of such path. As a basis, we use it to compute the motion's radius.

## Step 3: Magnetic Field

The challenge is to find the needed magnetic field.

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